Large-scale Structure Formation Research Articles

Large eddy simulations of unsteady non-reaction flow characteristics using different geometrical combustor models

Large eddy simulations and power spectral density methods are used to investigate the unsteady non-reaction flow characteristics, as an important phenomenon in the combustor. The simulated was consistent with experimental velocity components and verified the effectiveness of this method. In the present work, four different geometric models of the combustion chamber were tested to assess the effects of primary holes and dilution holes on the contributions of unsteady features. The results reveal that vortex structures and pressure oscillations in turbulent field are enhanced because the primary and dilution holes exist. The dominant mechanisms that drive the non-unsteady instability are attributed to the formation of large-scale vortex structures. The oscillation amplitudes are affected by the primary and dilution holes. When the primary and dilution holes is eliminated from the combustor, the pressure oscillation amplitudes decrease. The research results are beneficial to further understand the unsteady non-reaction flow characteristics of geometrical combustors.

Eigenmode analysis of perturbations in the primordial medium at and before recombination

Context. Anisotropies of the cosmic microwave background are thought to be due to perturbations of the primordial medium, which, post recombination, lead to the formation of galaxy clusters and galaxies Aims. The perturbation wave modes of the primordial medium at and before recombination, consisting of a fully ionised baryonic plasma, a strong black body radiation field, and cold dark matter, are analysed. Methods. We use the linear perturbation theory of the relativistic equations of motion, utilising a strict thermodynamic equilibrium model that relates the radiation energy density to the plasma temperature. Results. It is shown that a wave mode corresponding to the postulated baryon acoustic waves exists with a phase velocity close to the speed of light, but the participation of the dark matter in this mode is very small. Instead, the dark matter has its own dominant mode in the form of gravitational collapse, with very little participation by the baryonic plasma. Conclusions. In view of this very weak coupling between baryons and dark matter, the initial conditions postulated for computer simulations of large-scale structure and galaxy formation – which assume that after recombination, when galaxy formation is getting underway, baryon and dark matter density perturbations are spatially coincident and are equal in terms of fractional amplitude – may be unjustified. Additionally, the possible non-coincidence of baryon and dark matter perturbations at the last scattering surface has implications for the analysis of cosmic microwave background anisotropies.

The NuSTAR, XMM-Newton, and Suzaku View of A3395 at the Intercluster Filament Interface

Galaxy clusters are the largest virialized objects in the universe. Their merger dynamics and their interactions with the cosmic filaments that connect them are important for our understanding of the formation of large-scale structure. In addition, cosmic filaments are thought to possess the missing baryons in the universe. Studying the interaction of galaxy clusters and filaments therefore has the potential to unveil the origin of the baryons and the physical processes that occur during merger stages of galaxy clusters. In this paper, we study the connection between A3395 and the intercluster filament with NuSTAR, XMM-Newton, and Suzaku data. Since the NuSTAR observation is moderately contaminated by scattered light, we present a novel technique developed for disentangling this background from the emission from the intracluster medium. We find that the interface of the cluster and the intercluster filament connecting A3395 and A3391 does not show any signs of heated plasma, as was previously thought. This interface has low temperature, high density, and low entropy, thus we suggest that the gas is cooling, being enhanced by the turbulent or tidal “weather” driven during the early stage of the merger. Furthermore, our temperature results from the NuSTAR data are in agreement with those from XMM-Newton and from joint NuSTAR and XMM-Newton analysis for a region with ∼25% scattered light contamination within 1σ. We show that the temperature constraint of the intracluster medium is valid even when the data are contaminated up to ∼25% for ∼5 keV cluster emission.

Large-Scale Cortex-Core Structure Formation in Brain Organoids

Brain organoids recapitulate a number of brain properties, including neuronal diversity. However, do they recapitulate brain structure? Using a hydrodynamic description for cell nuclei as particles interacting initially via an effective, attractive force as mediated by the respective, surrounding cytoskeletons, we quantify structure development in brain organoids to determine what physical mechanism regulates the number of cortex-core structures. Regions of cell nuclei overdensity in the linear regime drive the initial seeding for cortex-core structures, which ultimately develop in the non-linear regime, as inferred by the emergent form of an effective interaction between cell nuclei and with the extracellular environment. Individual cortex-core structures then provide a basis upon which we build an extended version of the buckling without bending morphogenesis (BWBM) model, with its proliferating cortex and constraining core, to predict foliations/folds of the cortex in the presence of a nonlinearity due to cortical cells actively regulating strain. In doing so, we obtain asymmetric foliations/folds with respect to the trough (sulci) and the crest (gyri). In addition to laying new groundwork for the design of more familiar and less familiar brain structures, the hydrodynamic description for cell nuclei during the initial stages of brain organoid development provides an intriguing quantitative connection with large-scale structure formation in the universe.

Beyond mass: detecting secondary halo properties with galaxy-galaxy lensing

ABSTRACTSecondary halo properties beyond mass, such as the mass accretion rate (MAR), concentration, and the half mass scale, are essential in understanding the formation of large-scale structure and dark matter haloes. In this paper, we study the impact of secondary halo properties on the galaxy-galaxy lensing observable, ΔΣ. We build an emulator trained on N-body simulations to model ΔΣ and quantify the impact of different secondary parameters on the ΔΣ profile. We focus on the impact of MAR on ΔΣ. We show that a 3σ detection of variations in MAR at fixed halo mass could be achieved with the Hyper Suprime Cam survey assuming no baryonic effects and a proxy for MAR with scatter <1.5. We show that the full radial profile of ΔΣ depends on secondary properties at fixed halo mass. Consequently, an emulator that can perform full shape fitting yields better than two times improvement upon the constraints on MAR than only using the outer part of the halo. Finally, we highlight that miscentring and MAR impact the radial profile of ΔΣ in a similar fashion, implying that miscentring and MAR need to be modelled jointly for unbiased estimates of both effects. We show that present-day lensing data sets have the statistical capability to place constraints on halo MAR within our assumptions. Our analysis opens up new possibilities for observationally measuring the assembly history of the dark matter haloes that host galaxies and clusters.

Radio footprints of a minor merger in the Shapley Supercluster: From supercluster down to galactic scales

Context. The Shapley Supercluster (⟨z⟩≈0.048) contains several tens of gravitationally bound clusters and groups, making it an ideal subject for radio studies of cluster mergers. Aims. We used new high sensitivity radio observations to investigate the less energetic events of mass assembly in the Shapley Supercluster from supercluster down to galactic scales. Methods. We created total intensity images of the full region between A3558 and A3562, from ∼230 to ∼1650 MHz, using ASKAP, MeerKAT and the GMRT, with sensitivities ranging from ∼6 to ∼100 μJy beam−1. We performed a detailed morphological and spectral study of the extended emission features, complemented with ESO-VST optical imaging and X-ray data from XMM-Newton. Results. We report the first GHz frequency detection of extremely low brightness intercluster diffuse emission on a ∼1 Mpc scale connecting a cluster and a group, namely: A3562 and the group SC 1329–313. It is morphologically similar to the X-ray emission in the region. We also found (1) a radio tail generated by ram pressure stripping in the galaxy SOS 61086 in SC 1329–313; (2) a head-tail radio galaxy, whose tail is broken and culminates in a misaligned bar; (3) ultrasteep diffuse emission at the centre of A3558. Finally (4), we confirm the ultra-steep spectrum nature of the radio halo in A3562. Conclusions. Our study strongly supports the scenario of a flyby of SC 1329–313 north of A3562 into the supercluster core. This event perturbed the centre of A3562, leaving traces of this interaction in the form of turbulence between A3562 and SC 1329–313, at the origin of the radio bridge and eventually affecting the evolution of individual supercluster galaxies by triggering ram pressure stripping. Our work shows that minor mergers can be spectacular and have the potential to generate diffuse radio emission that carries important information on the formation of large-scale structures in the Universe.

Evolution of Primordial Magnetic Fields during Large-scale Structure Formation

Primordial magnetic fields (PMFs) could explain the large-scale magnetic fields present in the universe. Inflation and phase transitions in the early universe could give rise to such fields with unique characteristics. We investigate the magnetohydrodynamic evolution of these magnetogenesis scenarios with cosmological simulations. We evolve inflation-generated magnetic fields either as (i) uniform (homogeneous) or as (ii) scale-invariant stochastic fields, and phase-transition-generated ones either as (iii) helical or as (iv) nonhelical fields from the radiation-dominated epoch. We find that the final distribution of magnetic fields in the simulated cosmic web shows a dependence on the initial strength and the topology of the seed field. Thus, the observed field configuration retains information on the initial conditions at the moment of the field generation. If detected, PMF observations would open a new window for indirect probes of the early universe. The differences between the competing models are revealed on the scale of galaxy clusters, bridges, as well as filaments and voids. The distinctive spectral evolution of different seed fields produces imprints on the correlation length today. We discuss how the differences between rotation measures from highly ionized regions can potentially be probed with forthcoming surveys.

Alternative ideas in cosmology

Some remarkable examples of alternative cosmological theories are reviewed here, ranging from a compilation of variations on the Standard Model through the more distant quasi-steady-state cosmology, plasma cosmology, or universe models as a hypersphere, to the most exotic cases including static models. The present-day Standard Model of cosmology, [Formula: see text]CDM, gives us a representation of a cosmos whose dynamics is dominated by gravity (Friedmann equations derived from general relativity) with a finite lifetime, large scale homogeneity, expansion and a hot initial state, together with other elements necessary to avoid certain inconsistencies with observations (inflation, nonbaryonic dark matter, dark energy, etc.). There are however some models with characteristics that are close to those of the Standard Model but differing in some minor aspects; we call these “variations on the Standard Model”. Many of these models are indeed investigated by some mainstream cosmologists: different considerations on CP violation, inflation, number of neutrino species, quark-hadron phase transition, baryonic or nonbaryonic dark-matter, dark energy, nucleosynthesis scenarios, large-scale structure formation scenarios; or major variations like a inhomogeneous universe, Cold Big Bang, varying physical constants or gravity law, zero-active mass (also called “[Formula: see text]”), Milne, and cyclical models. At the most extreme distance from the Standard Model, the static models, a noncosmological redshift includes “tired-light” hypotheses, which assume that the photon loses energy owing to an intrinsic property or an interaction with matter or light as it travels some distance, or other nonstandard ideas. Our impression is that none of the alternative models has acquired the same level of development as [Formula: see text]CDM in offering explanations of available cosmological observations. One should not, however, judge any theory in terms of the number of observations that it can successfully explain (ad hoc in many cases) given the much lower level of development of the alternative ones, but by the plausibility of its principles and its potential to fit data with future improvements of the theories. A pluralist approach to cosmology is a reasonable option when the preferred theory is still under discussion.

The cosmological simulation code CONCEPT 1.0

ABSTRACT We present version 1.0 of the cosmological simulation code $\rm{{\small CO}{{\small N}}{\small CEPT}}$, designed for simulations of large-scale structure formation. $\rm{{\small CO}{\rm{\small N}}{\small CEPT}}$ 1.0 contains a P3M gravity solver, with the short-range part implemented using a novel (sub)tiling strategy, coupled with individual and adaptive particle time-stepping. A primary objective of $\rm{{\small CO}{\rm{\small N}}{\small CEPT}}$ is ease of use. To this end, it has built-in initial condition generation and can produce output in the form of snapshots, power spectra, and direct visualizations. $\rm{{\small CO}{\rm{\small N}}{\small CEPT}}$ is the first massively parallel cosmological simulation code written in Python. Despite of this, excellent performance is obtained, even comparing favourably to other codes such as gadget at similar precision, in the case of low to moderate clustering. By means of power-spectrum comparisons we find extraordinary good agreement between $\rm{{\small CO}{\rm{\small N}}{\small CEPT}}$ 1.0 and gadget. At large and intermediate scales the codes agree to well below the per mille level, while the agreement at the smallest scales probed ($k \sim 13\ h\, {\rm Mpc}^{-1}$) is of the order of 1 per cent. The $\rm{{\small CO}{\rm{\small N}}{\small CEPT}}$ code is openly released and comes with a robust installation script as well as thorough documentation.

Galaxy Flows within 8000 km s−1 from Numerical Action Methods

Abstract The trajectories since z = 4 of systems of galaxies (“halos”) with cz < 8000 km s−1 are found through numerical action reconstructions. A set of 9719 halos from a Two Micron All Sky Survey group catalog and Cosmicflows-3 catalogs are given attention. Present distances are adjusted to minimize departures from observed redshifts. For those with the most precisely determined distances, compromises are made between distance and redshift agreement. H 0 is varied from 69 to 77 km s−1 Mpc−1, with Ω m set by the baryon acoustic oscillation constraint from the Planck satellite. A best-fitting amplitude of the mass-to-light relation is found. A uniform density associated with the interhalo medium accounts for the matter not in halos. The solution paths provide the histories of the formation of the nearby large structures and depict how the voids emptied. Assuming no local over/underdensity, the best model has H 0 = 73 km s−1 Mpc−1, with nearly the same density arising from interhalo matter (IHM) as from halos. We examine local over/underdensities by varying the IHM density and find a valley of best-fit models along H 0 = 73.0(1 + 0.165δ) km s−1 Mpc−1. Friedmann models with distinct densities internal and external to the study region give a similar relationship. The fraction of matter in the IHM seen in n-body simulations roughly matches that in our H 0 = 72 scenario. Videos have been created to visualize the complexities of formation of large-scale structures. Standard n-body calculations, starting from the first time steps as tests of the numerical action method solutions and continuing until cosmic scale factor a = 2, provide glimpses into the future.

Impact of Warm Dark Matter on the Cosmic Neutrino Background Anisotropies

The Cosmic Neutrino Background (CνB) anisotropies for massive neutrinos are a unique probe of large-scale structure formation. The redshift-distance measure is completely different for massive neutrinos as compared to electromagnetic radiation. The CνB anisotropies in massive neutrinos grow in response to non-relativistic motion in gravitational potentials seeded by relatively high k-modes. Differences in the early phases of large-scale structure formation in warm dark matter (WDM) versus cold dark matter (CDM) cosmologies have an impact on the magnitude of the CνB anisotropies for contributions to the angular power spectrum that peak at high k-modes. We take the examples of WDM consisting of 2, 3, or 7 keV sterile neutrinos and show that the CνB anisotropies for 0.05 eV neutrinos drop off at high-l multipole moment in the angular power spectrum relative to CDM. At the same angular scales that one can observe baryonic acoustical oscillations in the CMB, the CνB anisotropies begin to become sensitive to differences in WDM and CDM cosmologies. The precision measurement of high-l multipoles in the CνB neutrino sky map is a potential possibility for the PTOLEMY experiment with thin film targets of spin-polarized atomic tritium superfluid that exhibit significant quantum liquid amplification for non-relativistic relic neutrino capture.

The Cosmological Constant as Event Horizon

General Relativity allows for a cosmological constant (Λ) which has inspired models of cosmic Inflation and Dark Energy. We show instead that rΛ=3/Λ corresponds to an event horizon: a causal boundary term in the action. Our Universe is expanding inside its Schwarzschild radius rS=rΛ=2GM, which could have originated from a uniform free falling cloud of mass M that collapsed as a Black Hole (BH) 25 Gyrs ago. Such a BH Universe allows for large-scale structure formation without the need of Inflation or Dark Energy.

Merger rate density of stellar-mass binary black holes from young massive clusters, open clusters, and isolated binaries: Comparisons with LIGO-Virgo-KAGRA results

I investigate the roles of cluster dynamics and massive binary evolution in producing stellar-remnant binary black hole (BBH) mergers over the cosmic time. To that end, dynamical BBH mergers are obtained from long-term direct N-body evolutionary models of $\sim10^4M_\odot$, pc-scale young massive clusters (YMC) evolving into moderate-mass open clusters (OC). Fast evolutionary models of massive isolated binaries (IB) yield BBHs from binary evolution. Population synthesis in a Model Universe is then performed, taking into account observed cosmic star-formation and enrichment histories, to obtain BBH-merger yields from these two channels observable at the present day and over cosmic time. The merging BBH populations from the two channels are combined by applying a proof-of-concept Bayesian regression chain, taking into account observed differential intrinsic BBH merger rate densities from the second gravitational-wave transient catalogue (GWTC-2). The analysis estimates an OB-star binary fraction of $f_{\rm Obin}\gtrsim90$% and a YMC formation efficiency of $f_{\rm YMC}\sim10^{-2}$, being consistent with recent optical observations and large scale structure formation simulations. The corresponding combined Model Universe present-day, differential intrinsic BBH merger rate density and the cosmic evolution of BBH merger rate density both agree well with those from GWTC-2. The analysis also suggests that despite significant 'dynamical mixing' at low redshifts, BBH mergers at high redshifts ($z_{\rm event}\gtrsim1$) could still be predominantly determined by binary-evolution physics. Caveats in the present approach and future improvements are discussed.

Influence of pipeline geometry on hydrodynamics and heat transfer processes by an example of a ship steam generator

The theoretical and computational analysis proposed in this work is aimed at identifying the features of thermal and hydrodynamic processes carried out in the steam-generating channels of the ship type water-moderated nuclear power installations. It is shown that the complex geometry of the thermohydraulic tract curvilinear channels of the steam generating system has a significant effect on the efficiency of the transport nuclear power installation. In addition to the formation of large-scale vortex structures and swirling flow in the pipeline, the phenomenon of the swirling flow crisis is revealed, under which the low-frequency component of the acoustic spectrum is enhanced. The scientific and applied significance of the proposed research is associated with the need to ensure a wide range of operational changes in efficient and safe operation power modes of icebreaker nuclear power installations. The research, aimed at developing the principles of physical and mathematical modeling of complex vortex flows, is necessary to optimize the design parameters of the thermal power equipment elements of new generation ship nuclear power installations in order to ensure increased safety and reliability of their operation.

Backreaction from inhomogeneous matter fields during large-scale structure formation

We study how inhomogeneities of the cosmological fluid fields backreact on the homogeneous part of energy density and how they modify the Friedmann equations. In general, backreaction requires to go beyond the pressureless ideal fluid approximation, and this can lead to a reduced growth of cosmological large-scale structure. Since observational evidence favors evolution close to the standard growing mode in the linear regime, we focus on two-component fluids in which the nonideal fluid is gravitationally coupled to cold dark matter and in which a standard growing mode persists. This is realized, e.g., for a baryonic fluid coupled to cold dark matter. We calculate the backreaction for this case and for a wide range of other two-fluid models. Here the effect is either suppressed because the nonideal matter properties are numerically too small, or because they lead to a too stringent UV cutoff of the integral over the power spectrum that determines backreaction. We discuss then matter field backreaction from a broader perspective and generalize the formalism such that also far-from-equilibrium scenarios relevant to late cosmological times and nonlinear scales can be addressed in the future.

Cosmic Web-halo Connection between Twin Universes

Abstract Both simulation and observational data have shown that the spin and shape of dark matter halos are correlated with their nearby large-scale environment. As structure formation on different scales is strongly coupled, it is tricky to disentangle the formation of a halo from that of the large-scale environment, making it difficult to infer which is the driving force behind the correlation between halo spin/shape and the large-scale structure. In this paper, we use N-body simulations to produce twin universes that share the same initial conditions on small scales but that are different on large scales. This is achieved by changing the random seeds for the phase of those k modes smaller than a given scale in the initial conditions. In this way, we are able to disentangle the formation of halo and large-scale structure, making it possible to investigate how halo spin and shape correspond to the change of environment on large scales. We identify matching halo pairs in the twin simulations as those sharing the maximum number of identical particles within them. Using these matched halo pairs, we study the cross match of halo spin and the correlation with the large-scale structure. It is found that when the large-scale environment changes (eigenvector) between the twin simulations, the halo spin has to rotate accordingly, although not significantly, to maintain the universal correlation seen in each simulation. Our results suggest that the large-scale structure is the main factor to drive the correlation between halo properties and their environment.

The Correlation between Rotational Gravity and Magnetic Field of Celestial Body

The magnetic field of the earth plays an important role in the ecosystem, and the magnetic field of celestial bodies is also important in the formation of cosmic large-scale structures, but the origin and evolution of the celestial magnetic field is still an unresolved mystery. Many hypotheses to explain the origin have been proposed, but there are some insurmountable difficulties for each one. At present, the theory widely accepted in scientific society is the dynamo model, it says that, the movement of magnetofluid inside celestial bodies, which can overcome the Ohmic dissipative effect and generate persistent weak electric current and macroscopic magnetic field. However, this model needs an initial seed magnetic field, and the true values of many physical parameters inside the celestial body are difficult to obtain, and there is no stable solution to the large range of fluid motion. These are all difficulties for the dynamo model. Furthermore, it is difficult for the dynamo to explain the correlation between the dipole magnetic field and angular momentum of a celestial body. In this paper, by calculating the interaction between spin of particles and gravity of celestial body according to Clifford algebra, we find that a rotational celestial body provides a field Ωα for spins, which is similar to the magnetic field of a dipole, and the spins of charged particles within the celestial body are arranged along the flux line of Ωα, then a macroscopic magnetic field is induced. The calculation shows that the strength of Ωα is proportional to the angular momentum of the celestial body, which explains the correlation between the magnetic intensity and angular momentum. The results of this paper suggest that further study of the effects of internal variables such as density, velocity, pressure and temperature of a celestial body on Ωα may provide some new insights into the origin and evolution of celestial magnetic field.

Predicting rocker shoe parameters for reducing plantar pressure using machine learning methods

The formation and evolution of quadruple synthetic jets issuing into quiescent air are experimentally investigated. Four different configurations (monopole-like, dipole-like, quadrupole-like and 90-degrees-circularly-shifted-jets) have been studied by varying the phase lags between the ejection strokes of the four jets, at constant values of the source Reynolds and Strouhal numbers, equal to 4000 and 0.2, respectively. For each configuration instantaneous three-component in-plane velocity fields in the most relevant streamwise planes are measured with stereoscopic particle image velocimetry. The evolution of the turbulent jet flow is analyzed by the velocity field triple decomposition, thus separating the time-averaged component from the forced periodic oscillation and the turbulent fluctuation. It is observed that the near region of the flow domain is dominated by the formation and advection of large-scale coherent vortex structures, which are originated by the interaction of the vortex rings inherent to the single synthetic jets. The vortex dynamics is captured by phase-averaged measurements and its role in determining the flow field structure of each of the investigated configurations is widely discussed. The vortex structures are observed to lose their coherence and break down into turbulence while propagating downstream. The decay of the large-scale coherent motions is accompanied by the establishment of a self-preserving behavior of both the mean flow and turbulent quantities. Nevertheless, it is shown that the far-field topology depends critically on the source conditions and near-field evolution.

The effect of Schmidt number on gravity current flows: The formation of large-scale three-dimensional structures

The Schmidt number, defined as the ratio of scalar to momentum diffusivity, varies by multiple orders of magnitude in real-world flows, with large differences in scalar diffusivity between temperature, solute, and sediment driven flows. This is especially crucial in gravity currents, where the flow dynamics may be driven by differences in temperature, solute, or sediment, and yet the effect of Schmidt number on the structure and dynamics of gravity currents is poorly understood. Existing numerical work has typically assumed a Schmidt number near unity, despite the impact of Schmidt number on the development of fine-scale flow structure. The few numerical investigations considering high Schmidt number gravity currents have relied heavily on two-dimensional simulations when discussing Schmidt number effects, leaving the effect of high Schmidt number on three-dimensional flow features unknown. In this paper, three-dimensional direct numerical simulations of constant-influx solute-based gravity currents with Reynolds numbers 100≤Re≤3000 and Schmidt number 1 are presented, with the effect of Schmidt number considered in cases with (Re,Sc)=(100,10), (100,100), and (500, 10). These data are used to establish the effect of Schmidt number on different properties of gravity currents, such as density distribution and interface stability. It is shown that increasing Schmidt number from 1 leads to substantial structural changes not seen with increased Reynolds number in the range considered here. Recommendations are made regarding lower Schmidt number assumptions, usually made to reduce computational cost.

Stability analysis of open-channel flows with secondary currents

This paper presents some results coming from a linear stability analysis of turbulent depth-averaged open-channel flows (OCFs) with secondary currents. The aim was to identify plausible mechanisms underpinning the formation of large-scale turbulence structures, which are commonly referred to as large-scale motions (LSMs) and very-large-scale motions (VLSMs). Results indicate that the investigated flows are subjected to a sinuous instability whose longitudinal wavelength compares very well with that pertaining to LSMs. In contrast, no unstable modes at wavelengths comparable to those associated with VLSMs could be found. This suggests that VLSMs in OCFs are triggered by nonlinear mechanisms to which the present analysis is obviously blind. We demonstrate that the existence of the sinuous instability requires two necessary conditions: (i) the circulation of the secondary currents $\omega$ must be greater than a critical value $\omega _c$ ; (ii) the presence of a dynamically responding free surface (i.e. when the free surface is modelled as a frictionless flat surface, no instabilities are detected). The present paper draws some ideas from the work by Cossu, Hwang and co-workers on other wall flows (i.e. turbulent boundary layers, pipe, channel and Couette flows) and somewhat supports their idea that LSMs and VLSMs might be governed by an outer-layer cycle also in OCFs. However, the presence of steady secondary flows makes the procedure adopted herein much simpler than that used by these authors.